WASHINGTON — The White House publicly acknowledged on Tuesday that President Biden did not expect to meet his goal of having 70 percent of adults at least partly vaccinated by July 4 and instead would reach that milestone only with people older than 26.

It would be the first time that Mr. Biden has failed to meet a vaccination goal he has set. If the rate of adult vaccinations continues on the current seven-day average, the country will come in just shy of his target, with about 67 percent of adults having at least one shot by July 4, according to a New York Times analysis.

White House officials have argued that falling short by a few percentage points is not significant, given all the progress the nation has made against Covid-19. “We have built an unparalleled, first-of-its-kind, nationwide vaccination program,” Jeffrey D. Zients, the administration’s pandemic response coordinator, said during a White House briefing. “This is a remarkable achievement.”

But health experts warn that the slowing vaccination rate could mean renewed coronavirus outbreaks this winter when cold weather drives people indoors, with high daily death rates in areas in which comparatively few people have protected themselves with shots.

“I give credit to the Biden administration for putting in place a mass vaccination program for adults that did not exist,” said Dr. Paul A. Offit, the director of the Vaccine Education Center at Children’s Hospital of Philadelphia. “But now we’ve hit a wall.”

Dr. Anthony S. Fauci, the nation’s top infectious disease expert, said at the White House briefing that “there is a danger, a real danger, that if there is a persistence of a recalcitrance to getting vaccinated that you could see localized surges,” or regional spikes.

He also warned of the rising prevalence of the Delta variant, first identified in India, which is more contagious than previous versions of the virus and may cause more severe disease. The variant now accounts for an estimated 20 percent of new infections, he said. A new analysis of nearly one-quarter of a million infections in the United States released Monday suggests the variant will soon be the dominant form of the virus here.

The three vaccines authorized in the United States are effective against the Delta variant, and Dr. Fauci said its spread lent new urgency to the campaign to vaccinate as many Americans as soon as possible.

Data released by the administration this week shows that young adults are most reluctant to get vaccinated. “Where the country has more work to do is particularly with 18 to 26 year olds,” Mr. Zients said. Many of them, he added, feel “like Covid-19 is not something that impacts them, and they’ve been less eager to get the shot.”

According to a Centers for Disease Control and Prevention report released Monday, just over one-third of adults ages 18 to 39 reported being vaccinated. In that group, those who were either 24 or younger, as well as non-Hispanic Black people and those with lower incomes, less education and no health insurance had the lowest reported vaccination rates and expressed the least interest in getting vaccinated, the report said. They most often cited concerns about the safety and effectiveness of the vaccines.

Mr. Zients said it would take “a few extra weeks” beyond July 4 to reach enough young adults to achieve the goal of 70 percent of adults at least partly vaccinated. But Dr. Fauci stressed that 70 percent “is not the goal line, nor is it the end game.”

A certain percentage of Americans are simply adamantly against the vaccine, said Dr. Marcus Plescia, the chief medical officer of the Association of State and Territorial Health Officials. “But I think there’s still people out there who are kind of on the fence about it and that’s where our opportunity is,” he added.

In announcing the goal on May 4, Mr. Biden made a personal plea to the unvaccinated, saying getting a shot was a “life and death” choice. According to the latest figures from the C.D.C., 150 million Americans — 45 percent of the population — have been fully vaccinated and 177 million have received at least one dose.

In recent weeks, new infections, hospitalizations and deaths related to the virus have declined sharply nationwide. As of Monday, the seven-day average of new virus cases across the United States was 11,243 cases a day, a decrease of nearly 30 percent over the last two weeks, according to a Times database.

Lazaro Gamio contributed reporting.